Maybe now that they have disposed of the aggravating and agitating Flyers — who always seem like an annoying sibling rival to them because of the teams’ familiarity with each other and their geographic proximity — it will liberate the Rangers for bigger and better things in these NHL playoffs.

Maybe now the Rangers make a real consistent, concerted run in this postseason — a run at a first Stanley Cup in 20 years — instead of acting like a car that sometimes starts at the first turn of the key and sometimes doesn’t, the way they looked too often in the Philadelphia series.

Perhaps Wednesday night’s 2-1 now-we-can-exhale win over the Flyers in Game 7 at the Garden propels the Rangers in their next series — against the Penguins, who will be favored to win, having finished with 13 more points in the regular season and with the home-ice edge.

There is not a Rangers fan alive who would not agree that a loss in this Philadelphia series would have rendered this season an essential waste of more than seven months. They fired their coach, the irascible John Tortorella, after last season for not getting them to the Stanley Cup and replaced him with Alain Vigneault, a coach whose demeanor is so calm, he sometimes appears catatonic.

A one-and-done postseason would have been beyond distasteful for hungry Rangers fans, who might have preferred they hadn’t made the playoffs, instead of losing to the Flyers with home-ice advantage and Henrik Lundqvist in net.

“If you lose in the first round, it definitely feels like a waste of a year to play 82 games and not move on,’’ forward Dan Carcillo said after scoring the Rangers’ first goal Wednesday night. “Everyone wants to make a run. That’s what we’re here for. That’s why you play the 82.’’

Carcillo, a former Flyer who won a Stanley Cup with the Blackhawks last season and was acquired by the Rangers in January, said he “knew’’ the Philadelphia series “was going to be tough and I figured it was going to go to seven games.’’

“It just came down to one hockey game,’’ he said.

One hockey game that had such a major impact on how this season is viewed.

“Losing in the first round, it’s like you make the playoffs but you don’t really get to enjoy the playoffs,’’ center Brad Richards said. “Now we’re in the middle of it and we’re in the battle. This is when it gets real fun. This was a great accomplishment. We won’t rest on it too much, but this is big.’’

Asked when the focus shifts to Pittsburgh, Richards, speaking at about 10:30 p.m., said, “Probably by midnight.’’

“Go home, get some food, talk about this a little, get some sleep and get back to work,’’ he said. “It’s hard to believe, but Philly is out of our minds now, and we’ve got to think about Pittsburgh.’’

Should we expect to see a better, looser, more liberated and offensively potent Rangers team against Pittsburgh than we saw against Philly?

“Usually, with the teams that keep going, that’s what happens — they get better,’’ Richards said. “That’s our goal. Each playoff round you’ve got to raise the level. The next series is going to be faster, it’s going to be more intense. Hopefully, we’ll set the bar in the first game and try to get [the Penguins] to our level. That’s your goal in each game and each series.’’

The Rangers do not depart this Philadelphia series and embark on the next round against Pittsburgh without issues that need resolving.

They cannot sweep away the fact their power play was 3-for-29 against the Flyers, including 0-for-the-last-21.

They cannot ignore the fact Rick Nash (one goal in 19 playoff games as a Ranger) cannot buy a goal — even if he had James Dolan’s debit card and ATM code.

They also cannot pretend they haven’t noticed their novice handling of prosperity, having lost an NHL-record 11 consecutive games when leading in a playoff series, dating to 2009. The Rangers with a series lead are like a college kid with his first credit card — carelessly spending without realizing there’s a bill that needs to be paid at the end of the month.

All of that said, though, perhaps the Rangers can clean up those blemishes now that they have dispensed with the pesky Flyers and rid themselves of that pressure of not being bounced from the first round.

“For sure, this was a real important game for us,’’ said Mats Zuccarello, who assisted on the Carcillo goal. “Everyone in here knows we are a good team, and if we play the right way, we can beat anyone. If we want to win a Stanley Cup, we had to get through the first round.’’

And so they did.

Now let’s see where this takes them, how deep they can take this playoff run, how special they can make this season now that the first round and the Flyers are out of the way.